Rank of an elliptic curve over the rational numbers by
Ciro Santilli 32 Updated 2024-09-07 Created 1970-01-01
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Mordell's theorem guarantees that the rank (number of elements in the generating set of the group) is always well defined for an elliptic curve over the rational numbers. But as of 2023 there is no known algorithm which calculates the rank of any curve!
TODO list of known values and algorithms? The Birch and Swinnerton-Dyer conjecture would immediately provide a stupid algorithm for it.